Solid phase carriers for multiplexed analysis of multiple analytes, preferably are encoded using one of several available color coding methods (see U.S. Ser. No. 09/448,420, filed Nov. 23, 1999, entitled “Color-Encoding and In-Situ Interrogation of Matrix-Coupled Chemical Compounds”; U.S. Ser. No. 10/348,165, filed Jan. 21, 2003, entitled “Method of Controlling Solute Loading of Polymer Microparticles,” U.S. Pat. No. 4,499,052 “Apparatus for Distinguishing Multiple Subpopulations of Cells) to produce spectrally distinguishable carriers; or using chemical tagging methods such as those commonly employed for encoding of combinatorial libraries to produce carriers distinguishable by way of decoding these tags by one of several methods known in the art (see, e.g., U.S. Pat. No. 6,503,759 “Complex Combinatorial Chemical Libraries Encoded with Tags”). In applications of interest, solid phase carriers are functionalized to display chemical entities such as nucleic acid probes or protein receptors, each such entity being uniquely associated with a code and defining a carrier type. Preferably, the molecular analysis of multiple analytes is performed in accordance with the Random Encoded Array Detection (READ™) format, as described in U.S. application Ser. No. 10/204,799, filed on Aug. 23, 2002, entitled “Multianalyte Molecular Analysis Using Application-Specific Random Particle Arrays” using microparticles (“beads”) as the solid phase carriers.
A method of encoding by providing multiple instances (“multiplicities”) of each distinguishable type of carrier within a set of N such types has been described in connection with a flow cytometric multiplexed immunoassay format (See U.S. Pat. No. 5,567,627—Lehnen). Although Lehnen states that larger numbers of analytes may be analyzed with this method, the examples relate to small numbers, N, of analytes, where N ranges from 2 to 4.
However, the molecular analysis of multiple analytes, and particularly the analysis of nucleic acid sequences, generally must accommodate numbers of analytes in the range of tens of analytes, or about 10≦N≦100. An example is the multiplexed analysis of the 25 mutations in the cystic fibrosis transmembrane regulator gene designated by the American College of Medical Genetics (ACMG) for pan-ethnic carrier screening, requiring at least 25 pairs of probes to discriminate normal and variant alleles.
To ensure an unambiguous decoding, application of the method in Lehnen for use in a method of encoding carriers requires a unique decomposition of N into summands, mk, such that no partial sum obtained by adding two or more summands can be obtained in any other way of combining summands, and no summand is itself the sum of two or more of the other summands. For example, if N=10 analytes are to be displayed on uniquely coded carriers, one might select ten prime numbers in an attempt to construct a unique set of multiplicities as required by Lehnen, e.g.: m1=5, m2=7, m3=11, m4=13, m5=17, m6=19, m7=23, m8=29, m9=31, m10=37, only to discover that this prescription fails, even for this value of N=10, given that m1+m4=m2+m3 and other non-unique combinations, which can be seen. Therefore, the task of constructing a unique decomposition for any N represents a problem to which Lehnen does not provide a solution.
Additional difficulties arise when consideration is given to practical requirements in assay design. For example, in typical quantitative assays which may produce, for each of several types of constituent probes, signal intensities varying over a wide range, the respective mean signal intensities generally will not be known a priori. Thus, even in the case of only two different types of carriers, when the standard deviation of the assay signal produced by the multiple instances of the first type of probe is comparable to the difference in mean signal intensities of first and second types of probes, codes will be corrupted, decoding will be compromised and assay scores will be indeterminate. Assay signal intensities have been observed to vary by 10% to 30% about the mean over a specific carrier type.
Additional practical requirements place further constraints on practical codes. Thus, each mk is bounded from below as a result of placing confidence intervals on assay scores. As described in greater detail below, this constraint, the random encoded array (READ™) format or equivalent assay formats, requires minimal multiplicities in the range of 30-50 to ensure desirable confidence intervals on assay determinations. Each mk also is bounded from above by the fact that the total number of carriers, M, readily accommodated in a practical assay format and thus typically in the range of ˜100 to ˜10,000, is finite, where M=Σ(k=1) to (k=N) mk, implying an upper limit for each of the mk. Further, in practice, the number of carriers of any given type contained in aliquots of suspension of nominally equal volumes will display a statistical variation, requiring that values of individual multiplicities be selected so as to differ from one another by at least several standard deviations about each mean, and thus not be spaced too closely. The methods described in Lehnen, therefore, do not enable multianalyte molecular analysis and also are not practical or desirable as a means of carrier encoding.
However, when number coding (“N-coding”) is augmented by an additional code—such as chemical coding and specifically color coding (“C-coding”)—and when applied to represent a finite, known number of outcomes for each of a multiplicity of probe types included in a multiplexed analysis, it is practical and desirable. In a multiplexed analysis of molecular analytes, N-coding permits the representation of a finite number of known or anticipated assay scores or outcomes for each of a multiplicity of types of probes or receptors included in the analysis. N-coding thus can be used to discriminate nucleic acid alleles by N-coded subtypes of carriers, each subtype displaying a probe matched to one of the known or anticipated alleles; specifically, N-coding can be used to discriminate normal and variant alleles by pairs of probes, one of these complementary to the normal (“wildtype”, W) allele and represented by a multiplicity mW, the other complementary to the variant (“V”) allele and represented by a multiplicity mV, where mV≠mW but both alleles share one color code. N-coding also can be used to discriminate epitopes by N-coded subtypes of carriers, each subtype displaying a receptor capable of binding to one of the known or anticipated epitopes of a ligand of interest, all such epitopes or ligands sharing one color code.